Gilles Lebeau

Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary

For the observation or control of solutions of second-order hyperbolic equation in

Complex immersions and Quillen metrics

\mathbb{R}_t \times \Omega

Stabilization and control for the subcritical semilinear wave equation

, Ralston’s construction of localized states [Comm. Pure Appl. Math., 22 (1969), pp. ...

A wave problem in a half-space with a unilateral constraint at the boundary

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Global existence for energy critical waves in

In this paper, we analyze the exponential decay property of solutions of the semilinear wave equation in R3 with a damping term which is effective on the exterior of a ball. Under suitable and natural assumptions on the nonlinearity we prove that the exponential decay holds locally uniformly for finite energy solutions provided the nonlinearity is subcritical at infinity. Subcriticality means, roughly speaking, that the nonlinearity grows at infinity at most as a power p<5. The method of proof combines classical energy estimates for the linear wave equation allowing to estimate the total energy of solutions in terms of the energy localized in the exterior of a ball, Strichartzs estimates and results by P. Gerard on microlocal defect measures and linearizable sequences. We also give an application to the stabilization and controllability of the semilinear wave equation in a bounded domain under the same growth condition on the nonlinearity but provided the nonlinearity has been cut-off away from the boundary.

3

In this paper, we study the following problem: let

-d domains

\Omega

Analysis of the HUM Control Operator and Exact Controllability for Semilinear Waves in Uniform Time

be a half-space of

Singular Optimal Control for a Transport-Diffusion Equation

\mathbb{R}^N

Gradient discretization of hybrid dimensional Darcy flows in fractured porous media

, defined by